Method and apparatus tor grinding



March 13,1945. B. LIEBOWITZ 2,371,303

METHOD AND APPARATUS FOR GRINDING LENSES Filed Sept; 18, 1942 5 Sheets-Sheet 1 ll TTORNO'S.

March 13 1945.

B. LlEBOWlTZ 2,371,303

METHOD AND APPARATUS FOR GRINDING LENSES Filed Sept. 18, 1942 3 Sheets-Sheet 2 I N VEN TOR.

ATToRnus March 13, 1945. Y B. LIEBOWITZ 2,371,303

METHOD AND APPARATUS FOR GRINDING LENSES Filed Sept. 18, 1942 3 Sheets-Sheet 3 INVENTOR.-

ATTORNCVS.

Patented Mar. 13,1945

, METHOD AND APPARATUS FOR. GRINDING LENSES Benjamin Liebowit z, Lewisboro, N. Y. Application September 18, 1942, Serial No. 458,843

13 Claims.

This invention relates to methods'and apparatus for the grinding and polishing of lenses. In current practice, after the lens blanks have been rough ground and smooth ground by hand operations, it is customary to mount the partly finished lens on a block by means of pitch. The block is then placed on' a rotating spindle and the-exposed surface is fine ground by means of an Oscillating lap, after which it is carefully cleaned to remove all abrasive particles and transferred to a polishing spindle. After the polishing of this exposed surface has been completed, the lens is removed from the block, soaked in alcohol to remove the pitch, varnished or shellackedon the finished surface, re-mounted on a block with the varnished surface against the pitch, and the above mentioned operations of fine grinding and polishing are repeated.

quality; that is to S y. by my method and apparatus it is less difficult to obtain precision surfaces than by conventional methods, for reasons which will hereinafter be set fort The objects of my invention are to" gain the advantages set forth and to achieve other ends as will hereinafter be explained.

In the accompanying drawings which form part of this specification,

Figure 1 is a diagrammatic view through a conventional lap operating on one surface of a lens conventionally mounted on a block;

Fig. 2a is a diagrammatic view showing two it has undergone an appropriate displacement;

After the second surface has been polished, the

lens must again be removed from the block, soaked in alcohol toremove the pitch and the varnish, and is then ready for the edging operation.

In my improved method and with my improved apparatus, both surfaces of the lens are operated von simultaneously and the mounting of the lens on a block is eliminated; in fact, all use of pitch is eliminated except in so far as pitch laps ma be used'for the-polishing operation.

The production advantage of my method is obvious where the lenses are such that they are ordinarily fine-ground and polished singly. In

the case of small lenses such that the solid angle subtended by the lens surface is small, it is customary in ordinary methods to mount a plurality of like lenses on oneblock simultaneously, so that a material advantage is gained in the current method by finegrinding and polishing a group of lenses at a time, where that is feasible. However, the time required to polish out a group of lenses of this sort is generally much longer than the time required to polish out the lenses individually, so that, although there is a substantial gain in group flneing and polishing,

"nevertheless the gain is not by any means proportional to the-number of lenses in the group. On this account, in many cases even as to. such small lenses, my method and machine 'ofier a production advantage over conventional group processing because of the gain in time and space resultingfrom the elimination of necessity of the mounting of the lenses on heads; as'well as from the fact that both surfaces of the lens are worked simultaneously. My method and apparatus offer certain other advantages which result in improved Figs. 3a and 3b are corresponding diagrammatic views of the application of my invention to a bi-convex lens with equal surface radii;

Figs. 4a and' 4b are corresponding diagrammatic views of theapplication of my invention to a plane-convex lens;

Figs.5a and 5b are corresponding diagram- 'matic views of the application of my invention of Fig. 6 and viewed in the direction ofthe arrows;

Fig. 8 is a cross-section through the gear box,

taken at right angles to the cross-section shown in Fig. 6, and Fig. 9 to a, top plan view of the gear box;

Fig. 9a is a bottom and associated parts;

Fig. 9b illustrates diagrammatically the mo tion imparted by the gearbox to the driving member for one of the laps used in machines embodying my invention; and

Fig. 10 shows an elevation partly in section, and Fig. 11 a plan along line ll-|l of Fig. 10 of a modified mechanism adapted to the "parallel" case of Figs. 3a, 3b.

The conventional system as shown diagrammatically in Fig. 1 will be briefly described in plan view of the "gear box order to bring out certain force relationships. The lens I is mounted by means of the pitch layer. 2 on the head 3. Pressed against thelens by means of the ball pin 5 ,is the lap 4. The ballpin 5 is carried in the boss 6 of an arm (not shown) which is oscillated back and forth roughly parallel to the plane of the drawing. The center of the lap surface and of the lens surface being ground or l olished is at C1. The ball 5a of the ballpin has its center at C2. in addition to the weights of theboss 6 and its arm, pin 5 and lap 4,,other weights or springs (not-shown) are frequently employed to increase the pressure between the lap and the lens.

In order to study the forces involved in this conventional system, let us first assume that the contact area between lens I and lap 4 is frictionless and likewise the contact area between the ball 5a and its socket in the lap 4. Under these circumstances, the pressure at the spherical sur faces is normal to those surfaces and the resultant force between the lens I and lap 4 is directed along the line C102; likewise the resultant force between the ball 5a and its socket is directed along the same line. This force has a lateral component which is imposed on the ballpin and which is taken up by the arm carrying the boss tion) and due to the fact that generally the line 6; in order to avoid confusion, this component is not indicated in Fig. 1. Now imagine that the oscillating'arm is traveling leftward, as shown by the arrow A-I, and consider the effect of the frictional forces. at the spherical surface of the lap 4. Since the lap is moving leftward, the frictional forces tend to push the lens leftward, and

the, corresponding reaction on the lap is to the right, as shown by the small arrows A2. These frictional forces will have a resultant force which is roughly indicated by the dotted arrow A-3 (plus a small couple which is generally negligible). In order to overcome this frictional force, there must be applied at the ballpin center C2 an equal and opposite force indicated by the arrow A-4. The forces A-3 and A-4 constitute a couple which tends to rock the lap 4; that is, it tends to lift the trailing end of the lap and to cause the leading edge of the lap to press harder on the lens I. This causes an-unequal distribution of pressure over the area of contact between lens and lap 4, and, if the coefficient of friction becomes sufflclently high, it will prevent the operation of the machine by actually rockingthe lap 4 against the vertical forces imposed by the ballpin 5, since the arm 6 which carries the ballpin 5 is free to move vertically. That is to say, frictional forces between the lens I and lap 4 give rise to a'force couple whose magnitude is equal to the product of the resultant frictional force times the approximate distance from the lens surface engaging lap 4 to the center C2 of the ballpin; this force couple gives rise to a nonuniform distribution of pressure between said lens surface and said lap; and it may under'extreme conditions of friction prevent operation of the machine entirely by actually rocking the lap 4 away from contact with the said lens surface except at one edge or the other where-it would tend to dig in. Corresponding analysis of the forces will be made hereinafter for a system operating under my improved method.

The frictional forces are not the only source of non-uniform pressure distribution between the lap 4 and the lens I. Due to the fact that the line of action of the impressed force is always directed along the lineCicz (disregarding fric- C1Cz does not pass through the center of the area of contact between the lens and the lap, the resulting pressure distribution can not be uniform. This second source,of non-uniform-pressure distribution is substantially unchanged in my improved method, but, under suitable operating conditions, it is not harmful.

Referring now to Fig. 2a, which is illustrative of principlesembodying my invention, II is a lens whose lower surface has the radius r1 centered at C1, and whose upper surface has the radius r2 centered at C2. [-2 is a lower lap having a spherical surface which is complemental to the lower surface of the lens, and I3 is an upper lap whose surface is complemental to the upper surface of said lens. I have chosen 1: greater than 11; Now, let us suppose that the upper lap is given an angular displacement about an axis passing through the center 01 and perpendicular to the plane of the sheet of drawing. This displacement will carry the lens H to the position shown in Fig. 2b and theupper lap into.

2b carrying its axis from the position C2 01 to the position Cz P. The angle of this displacement will be denoted by 112. a: is so chosen with respect to al that the linear movement of the two laps with respect to the lens surfaces will be the same, so that the grinding or polishing action will be the same. This condition is fulfilled if the.

formula is satisfied. Before the motion was begun, the two laps l2 and I3 were substantially co-axial with axes along the line C102. After the completion'of this displacement, the axis of the lower lap has remained undi'splaced while the axis of the upper lap has moved to the position C2 1.

The point P represents the intersection of the new axis of the upper lap with the original coaxis C102.

It will now be shown that the point P where the new and the 01d axes intersect is substantially constant, independent-of the angle, for angles of such magnitude as would be used in actual practice. It can be shown from trigonometry that the distance from the fixed center C1 of the lower lap to the'point P is given exactly by the following formula For sufficiently small angles, the sine of the angle may be replaced by the angle with a high degree ofaccuracy. Making this approximation, 1 ob-' tain, for small angles, the following formula (EEFWB E proximation.' To. obtain a, higher approximation valid for larger angles, I use two terms of the 4 series expansion for the sine of an angle, thus obtaining c P) 0 (4) (1 2 12 1 T122 1- 1-E a whence using Formula 3 I get where the subscript 2 on (Came-indicates that the distance is given by the formula to the second approximation. This approximation is sufficient- 1y precise for almost all practical purposes. It

Applying this formula to the special case, I get 2% for the distance C102. The first approximation using Formula 3 gives C 1P )1 as 1.375". The

second approximation using Formula 4 increases this distance by approximately of'1% to the value 1.383". For ordinary purposes, I may ignore this small variation in the position of. the

point P and regard P as a fixed or determined point in themo'tion of the system. I

In discussing Fig. 1 and'alsoFigs. 2a. and 2b, I have merely considered the oscillatory motion of the upper lap. It will be understood that the lower lap is rotated about its own axis continuously in Figs. 2c and 2b, just as it is in the case illustrated by Fig. 1.

The displacement obtained in passing from Fig. 2a to Fig. 2b may be regarded, then, as an angulardisplacement of the upper lap l3 about the point P. In an actual machine, presently t be described, the upper lap I3 is given a constrained motion about the point P, but this,mo--

tion-need not necessarily be an'oscillation. It may be, and in practice preferably is, a conical" in practice i lens surfaces and the respective surfaces of the laps l2 and I3 will again be directed along the vline C102 Since this line does not pass through the center of area of contact between either lens surface and its corresponding lap, a non-uniform pressure will arise from this source corresponding to the non-uniform pressure distribution due to the second cause discussed under Fig. 1. How.

(ever, the non-uniformity of pressure distribution 'due to the first cause discussed under Fig. 1' is very substantially reduced in my method, as will now be described.-

Again, let it be supposed that the upper lap C1 of Fig. 2b is being oscillated to the left, as indicated by the arrow-A" l of that figure. The frictional forces onthe upper surface of the lens will be directed as shown by the small arrows A.-2 (note that I am now discussing the frictional forces on the lens, whereas in Fig. 1 I was discussing the frictional-forces on the lap 4). There will be a corresponding'set of frictional forces on the lower surface of the lens ll indicated by the arrows A5. The resultants of the frictional forces A-2 and A-5 will now-be colinear, and all that remains are two couples mentioned parenthetically on page 2, line 39, as being generally negligible. Hence, there will be very little tendency arising from frictional forces to rock the lens ll the non-uniformity of pressure arising from this source is therefore minimized.

This circumstance represents by itself a material gain in quality, because'anything which tends to make the pressure .distribution between the lens and the lap non-uniform makes it more difficult to obtain optically precise surfaces and increases the operating time. The conical motion of lap l3 discussed above offers another advantage in this respect. In conventional machines such as shown in Fig. 1, the oscillation 'gives rise to a periodic reversal of direction of motion and hence to a corresponding reversal in the frictional forces. As a result of this, there is a very small but none I the less objectionable displacement of the lap 4 with respect to the lens I at the conclusion of each stroke. By using the conical motion for lap 13 as described above, this reversal of frictional forces is eliminated, and a correspondingly greater motion; that is to say, a'preferred form of motion is one in which the axis PO2 of the upperlap rotates about the line CiCz, said axis making an angle or minus a: with:the line C102. Moreover, as will be further discussed below, this angle is preferably varied slowlyduring the motion. In

any case, the motion of the lap 13 is rigidly determined by the machine elements, except for small displacements. from deflections and clearances and except for motion parallel'to its own axis. By means of a weight or a spring, an axial load is applied to the upper lap I3 and this load is 'freelytransmitted to the lens and to thelower lap because of the longitudinal freedom allowed the lap l3. Aside from smalljdeflections and clearances of the machine elements and the rotation about its stationary axis C102, the lower lap for the moment, the resultant forces between the smoothness and stability of motion is obtained which enhances the performance of the machine.

The basic kinematics of the system shown in Figs. 2a and 2b is fundamentally the same as that of the conventional system shown in Fig. 1. In the case of Fig. l, the position of the lap 4 at each point of the motion is uniquely determined except for possible slippage. Precisely the same remark applies to the lens in the system shown in Figs. 2a and 2b. That the latter system will actually function as I have here indicated will be shown I by a geometrical or kinematical demonstration in the next paragraph, but I may state first that I have used systems such as that of Figs. 2a and 2b and of Figs. 3a and 3b and that these uses show that such systems do function as described.

The kinematical behavior of any link having a ball joint at each end is, except for friction, com- .pletelydetermined by the ball centers and is m dependent of the diameters of the balls. Except for frictional forces, therefore, whose effects-have been fully discussed above and which may for present purposes be ignored, the lap 4 of Fig. 1 may be regarded as a ball jointed link, with the lens I and lap 4 constituting one balljoint and e the ball 5a and its socket in the lap 4 constituting The kinematic length of this ball jointed link is the distance between the centers the other.

- ball a increased in diameter and imagine its substance changed from steel to glass. The lap 4 still acts as a ball Jointed link. In this way, I have transformed Fig. 1 from a conventional lens machine to a new type of lens machine in which one surface of each. of two lenses 1 and 5a (transformed) is being operated upon simultaneously. Now imagine a further change in which the material of the lap 4 is changed from cast iron to glass and the elements I and So that were glass in the previous transform are changed to cast iron. This changes the first transform of Fig. 1 into a second transform which operates simultaneously on both surfaces of a bi-concave lens, with the lens itself now acting as the ball jointed link. In a similarway, it can be shown that the lens Ii itself .in Figs. 2a and 2b acts as a ball jointed link with centers at C1 and C2 (or C2 of those figures. The fact that the centers 01 and C2 (or C2) are, so to speak, inverted with respect to the positions of the centers in an ordinary ball jointed link, does not alter the kinematics. The following results of the discussion of this paragraph may be pointed out:

1. A lens machine is disclosed which operates 7 2. A lens machine is disclosed which operates simultaneously on both surfaces of a bi-concave lens.

3. The propositionhas been demonstrated that the systems disclosed herein will function as described, except in so far as frictional forces may interfere.

My system is most advantageously applied to lenses of relatively high curvature, but it can be employed on other types of lenses. Such lenses, it will be seen from the drawings Figs. 1-51), have a thickness at the center thatis substantially different from that at the edges.

I will now consider some of the other lens surfacecombinations shown in the drawings and show how the formulae (1-5 inclusive) given above may be applied to them. In Figs. 3a and 3b, I have shown a system which differs from the system of Figs. 2a and 2b in that both surfaces now have the same radius of curvature; that is to say, in the said formulae above, r1 becomes equal to T2. In this case, it can readilybe seen from formulae (3 or 4) that the point P moves oil to infinity because T2-Tl becomes zero in these formulae. This means that the required motion is an oscillation or rotation such that the angles a; and :12 are always equal; that is to say, the axes of the two laps i2, i3 of Figs. 3a and 3b remain parallel during the motion. Since this parallel motion is the limit of a conical motion( as P moves Zto infinity), it may still be properly called a conical motion. Fig. 3b has been constructed from Fig.

3a by the same steps as Fig. 2b was constructed from Fig. 2a, and requires no further description. Figs. 4a and 4b treat the case where one of the finity. The distance CiC-z likewise becomes in- Itcan be shown in this case that the Formulae 2 and 3 given above degenerate to the expression (for small angles) C1P=r1. Again, the point P in Fig. 4b acts as an approximately fixed center for the conical or oscillatory motion. In this case, the angle a: is zero; that is to say, in the surfaces is plane; that is, n is put equal to in- As a final example, I have shown in and 5b the case of a convex-concave lens. This case is derived from the formulae developed for Figs. 2a and 2b, mathematically speaking, by

making 1': negative. This makes the angle a: likewise negative. The appearances of the formulae .are unchanged by this change of sign, but in applying the formulae the negative sign must be used before 1'2. With these modifications, Fig, 5b is constructed from Fig. 5a by the same steps as Fig. 2b was constructed from Fig. 2a. Again, the point P of Fig. 5 represents an approximately fixed point which is the center of the conical rotation or oscillation. These examples will suffice to show how the method can be applied to other combinations of lens surfaces, such as piano-concave, bi-concave, etc.

It is not to be construed from the preceding description that the point P asdetermined by the above formulae or constructions is the point at which the center of the oscillatory or conical equal mechanical action on both surfaces of the,

lens; but, if for any reason one surface of the lens should grind out or polish out materially faster than the other, the setting can be changed by moving the motional center so as to increase the relative mechanical movement at the. face .where the grinding or polishing takes place more slowly.

Referring now to Figs. 6 to 9 inclusive, which illustrate a machine designed to carryout the operations indicated in the diagrams of Figs. 2a and 212, II is the lens which is being ground or polished, I2 is the lower lap and I3 is the upper lap, all corresponding with Figs. 2a and 2b. The upperiap i3 is attached removably, for example, by means of the taper shown, to a rod Mb which has a sliding fit in the bore of the member M, which in turn has a sliding fit in the bore of a sleeve IS; the member H may be provided with a key i5 operating in a keyway 16a in order to prevent the member l4 from rotating in said sleeve i8. However, I have obtained satisfactory results also in many cases by'dispensing with the key 15 and keyway lfia and allowing the member id to float; the rod Mb is acted on by the spring ilc; furthermore, the rod Mb has its longitudinal .motion limited by the head of. the screw 14d operating in the slot Me; the screw and slot arwhich have a bearing fit on the headed stud shaft or pin 20. The fork I8 is longitudinally positioned by the head of the pin 20 and the collar 2i, The outer end of the pin 20 is suitably clamped in the bracket 22 as by means of a split in said bracket and a clamping bolt 22a which Figs. 5d

' means of a force fit and planetary rotation about the pinion 32.

serves to tighten the bracket around said shaft or pin 20.

By the construction shown, the sleeve I6 is universally pivoted. The center of thissystem of pivots is provided by theintersection of the axis of shaft or pin with the axis of pins l1.

* This point of intersection'is indicated by P in Fig. 6 and corresponds to the center of motion or oscillation indicated by the in Fig. 2b. Any other pling of sleeve IE .to be used.

The upper end of the member or slider |4 terminates in a ball socket in which is seated the ball 23a of the ballpin 23. The ball is retained in its socket suitably as by means of the cap |4a conical point P suitable :un-iversal couprovide such center P may screwed onto the end of the slider 4. The ballpin 23 is rigidly held (as by means of a taper pin 23b shown in Fig. 8) in the swinging arm 24 which has a bearing fit on the shaft 25' and is held thereon by collar 25b. Washers 250 are employed as indicated to minimize friction and wear as the arm 24 swings backand forth on shaft 25.

The shaft25 has an extension 25a which protrucles through alower disc and threadedly engages in an upper disc 29. A suitable spacer 28 is provided on said extension 25a between said discs 29 and 38. Other'suitable bolts 21 and 28, each carrying similar spacers 25 tain the two discs in rigid fixed spaced apart relationship. These two discs 29 and 30, together with the gears to be described, constitute what I shall call, for'convenience, the gearbox.

A central pin 3| is rigidly attachedle. g., by

disc or plate 30. This pin has a bearing fit in in turn engages the suitably supported rod 44,

whose function is to prevent the arm 43 (and hence the pinion 32) from rotating. Meshing with the pinion 32: is the gear 33 which drives the member 34, which latter has a force fit in the gear 33. The -member 34 is rotatably supported by the discs 29 and 30 and acts as a shaft for the gear 33, and has an enlarged portion milled with a T slot 34a. The square head 35a of a bolt 35 fits slidably in this T slot. A flanged bushing 31 has a clearance fit on the pin 35. The outside diameter of this bushing 31 has abearing fit in a member 38. The parts '31 and 38 are so fitted that, when'the nut-36 is tightened on the bolt 35, they will be solidly clamped together with member 34 andyet permit free rotation of member 38 on the bushing 31. In this way, the pin 35 is locked in any adjusted position in the T slot 34a without binding member 38. Other suitable means for eflecting. this result may be employed. A slotted bar 4| is clamped at its'slotted end 4|a to an extension 38a of the member 38 (Fig. 9a) by means of bolt 39. When so clamped,

bar 4| and member 38 are rigid relative to each other. At its otherend, bar 4| is clamped similarly by bolt 40 to an extension 42a of the member 42 which has a bearing fit on the shank of the ballpin 23 and is otherwise similar tothe member 38. The members 38 and 42'and bar 4| to- SEI'VG t0 maina pin 3|a) to the lower means of the connecting rod assembly this ro- The lower lap I2 is removably held, for example by means of a taper connectiomon a cap member 5| which is threaded onto bearing 52 fitted with bushings 53, which have a bearing flt on the stationary hollow spindle 54. Spindle 54' is solidly attached, for example by means of a drive fit, to the flange 55. Clamped between the cap 5| and the bearing 52 is a cup 58 which is recessed to receive the head 51a of the rod 5! together with washers 58a above and below said head 51a, as indicated in the drawings. It vim be understood that the head 51a is free to turn in the cup 56; that is,- after the cup 58 is clamped between the cap-5| and the bearing 52, the head 51a will have both ance. The rod 51 has a threaded portion 51b which engages the corresponding thread. in the lower end of the stationary hollow spindle 54. The lower end 510 of handle 58. is raised or, lowered, thereby raising or lowering the cap-and-bearing assembly and with it the lower lap |2.' is provides a fine adjustment for bringing thecenter of curvature of the lower serving as a jam nut. The bearing member 52 gether constitute an adjustable connecting rod which connects the pin 35 to the ballpin 23.- By

means of this arrangement, as the discs 29 and 30 rotate as will be presently described, gear 33 has The member 34 rigid with gear 33 also rotates and the eccentric pin 35 is then rotated around the com-.

mon axis of the gear 33 and member 34, and by is provided with a pulley. The foregoing parts have been so designed that they may be readily attached to a commercial form of bench type drill press. Only such portlons of the drill press are shown in the drawings portion 52a which acts as a as are necessary to indicate how these parts are to be mounted. The drill press has a base 6| to which the flange is attached; for example by means of bolts not shown. In attaching flange 55 to the boss 6|,'it is desirable to bring the stationary spindle 54 into good alignment with the spindle of the drill press (not shown). The drill press has a post 82 which carries its upper mechanism (not shown) including its spindle. These drill presses are normally provided with a tilting table whichcan be adjusted vertically on the post by means of the part 63, and rotationally I by means of the stub 63a. The tilting table is removed and the stub 63a is used for mounting the bracket 22 on the drill press, said bracket being clamped on the stub 63a by means of a split and clamping bolt 22b. As usual, the spindle of the drill press carries at its lower'end the drill chuck 84. The central pin 3| of the gear box is fastened in the drill chuck in the same manner as a drill is fastened. The drill press is also normally provided with a collar (not shown) which moves up and down with the spindle but does not rotate with it. The rod 44 is attached to this collar and prevents the arm 43, hence the pinion 32, from rotating by engaging said arm as previously described.

It will be understood that the lower bearing assembly is rotated by means of a belt and the pulley portion 52a. Also; that the drill chuck 64 is rotated'in the conventional way. These two rotations may be in the same or opposite directions.

The means for achieving these rotations are conventional and need ,not be further described.

In order to apply the desired pressure, it is merely necessary to bring down the drill chuck 24 about the shaft radial and longitudinal clear- I connections described, carries the ballpin 23.

around an orbit which would be circular if said ball pin were held stationary in an eccentric position with respect to the gear box" (e. g., by adjusting the pin 35 in slot 34a to zero eccentricity relative to the axis of member 34) This circular motion would impart a conical motion to the slider l4, and from the construction of the mechanism, it is obvious that the center of this conical motion would be at the point P, as heretofore explained. However, the motion of the ballpin is not strictly circular but is in the form of a fspiral" which goes from maximum diameter to minimum diametenthen back to maximum again. cyclically. This spiral motion is produced as follows. As the drill chuck 64 rotates, it rotates the gear box discs 29 and 30 around, with it by means of the pin 3|. Now, since the pinion 32 does not rotate, the gear 33 acts like a planetary gear and is caused to rotate about its axis. If the gear ratio isn, then n revolutions of the gear box will be required for one spiraloycle. (Note that I am here concerned with the rotation of the gear 33 with respect to the gear box, and this is the same as that given by the ordinary gear ratio, no matter whether-pinion 32 rotates and the gear box is held stationary, or vice versa.) In the machine shown in the drawings, the value of n is nearly 3 (n should preferably not be an integer). As the gear 33 rotates on its axis, it rotates member 34 with it and carries the eccentric pin 35 around in a circular path, the radius of which depends upon the position of the pin 35 in the T slot 340;. This circular-motion of the eccentric pin 35 is communicated as an oscillatory motion to the ballpin 23, as heretofore, described, and the combined motions of the ballpin give rise to a compound conical motion of the slider. M such. that the cone 'angle varies periodically from maximum to minimum and back. The center of this compound conical motion is again at P.

The mean angle of the conical motion is adjusted by adjusting the length of the connecting rod, heretofore described; The amplitude of the cone angle variation is adjusted by adiusting the position of the pin 35 in the T slot 34a.

The arrangement of slider l4 and universally pivoted sleeve I6 is not suitable for .the parallel case, shown in Figs. 3a and 3b, for reasons heretoforeset forth. To provide for this case, the arrangement shown partially in section in Fig.

.10 and in plan in Fig. 11 is used. .The slider member I is unchanged including means for attaching the upper lap I3 and the ballpin 23, but instead of the universally pivoted sleeve IS, a pair of pivoted arms ll-I2 is employed.- The slider l4 slides in the boss Ha of the arm H, which may be provided with a keyway to receive the key l as before. At its other end. the arm The motion imparted to the slider H by the bell pin 23 driven as described is again a mean circle on which is superimposed a slow radial oscillation causing the motion to proceed as before in the form of ever-waning and waxing spirals between maximum and minimum limits prescribed bythe eccentricity of the pin 35. t

It may be pointed out that the parallel" arrangement of Figs. 10 and 11 may be employed, not only where the two lens surfaces are equal in radii, but also where they are nearly equal. It will be noted that in the formulae given earlier in this specification, the difference r2 minus n of the radii of the lens surfaces appears in the denominator for the expression giving the location of the point P with reference to the center of the lower lap surface. If 1'2 and T1 are nearly equal, the corresponding distance of the point P will be large .on this account.

When this distance is fairly large, no serious error arises in ordinary cases from regarding the point P as lying at infinity and using the parallel linkage instead of the conical linkage of Figs. 6 and 7. Moreover, as ,was pointed out above, it is not necessary for the satisfactory functioning of my machine that the actual center of oscillation or conical motion coincide closely with the theoretically determined point P.

In all-lens grinding and polishing operations,

it is necessary to use grinding or polishing media which, in conventional methods, are fed periodically to the surfaces being worked; e. g., by means of a brush. The method of finishing lens surfaces here proposed permits of a more efficient and less laborious wayof handling the grinding arid polishing media. For this purpose, I propose to employ a cup member 8| which may be carried on the lower lap l2 as indicated in Fig. 6, with the joint between 8| and I2 rendered watertight, e. g., by means of a wax layer 82, or in any other suitable way. The grinding or polishing compound is placed in the'cup at a suflicient height to cover the lens. The process of operating the machine will keep the mixture stirred; but, if this is not sufficient, additional stirring means (not shown) may be employed.- The grinding or polishing medium must, of course, be replenished and in particular evaporation must be allowed for, e. g., by adding small quantities of water at intervals. However, the attention which must be given to the machine, by the op-' erator is very much reduced by this method of Y feeding. Moreover, this method is less likely to give rise to unequal friction at the two lens surfaces.

The motion given to the upper lap l3 by the gear box and the slider M has been described as a conical motion centered at P, with the angle of the cone varying periodically from a minimum to a maximum and back. ratio; that is, by interchanging the positions of pinion 32- and gear 33, the motion becomes one which can be described as an oscillation with the plane of oscillation being continuously rotated. The latter type of motion has some advantages.

II is pivoted to the arm 12 by means of the lugs Ilb and pin 13. At itsfree end, the arm 12 is pivotally attached to the bracket 22 by pin II. By this construction, the slider I4 is constrained to remain parallel to itself .throughout its motion.

While I have described mechanisms for obtaining motions differing from the simple oscillatory motion conventionally used in lens grind- By inverting the gear I scription.

have found that the asvnsos son that such motions and the methods for producing them are too well-known to require description. Modifications of my machine necessary for obtaining such simple oscillatory motions will' be readily understood by any one skilled in the lens grinding art. Many other modifications are feasible, for example, the modification in which an oscillatory motion is employed as distinct from a conical motion) but in which the amplitude of oscillation is periodically varied as by means of a gear box structure similar to that shown in Figs. 8, 9 and 911. Furthermore, modifications in the adjustment or the design of the machine in order to accommodate it to other combinations of lens surfaces; for example, those shown in Figs. 4a to 5b inclusive, will also be readily understood and require no further de- There are a great many other modifications which may be made in the structure and operation of the machine. I To mention just a .few, I machine will operate with the gear box and upper driving mechanism completely eliminated and w th the center of the conical motion displaced off the axis of the lower spindle. Furthennore, I have found that, even when the center of the conical motion is approximately on the axis of the lower spindle, with the gear box removed as before, but with a-weight placed on the member l4, oscillations .f the upper mechanism may be self-induced. r, using the gear box, the lower lap may be held stationary or left free. Mention of these modifications is not to be construed as a limitation. i

While I have described my method as operating on both surfaces of a single lens, and asparticuiarly adapted for such purposes, it should not be construed that the method can not be applied to operations on a group of lenses corresponding to'the group method employed in conventional practice. By mounting two groups of lenses on a lenticular shaped block, one group being mounted rn each face of said block, my method may be employed to operate simultaneously on the expo-sod surfaces of the lensesof both of said rours. In this application, the advantage of the eiimi-iation of the pitch mounting of lenses on a block is lost but certain other advantages are gained. The word lens as usedin the c'aims shall be interpreted to mean either a single lens or a double group of lenses. Whether operating on two surfaces of a single lens or on the surfaces of two groups of lenses,

a characteristic of my machine is that the two laps have a relative oscillatory orconical movement centered at a point which is not at the center of any of the lens surfaces and whose location is determined approximately by Formula 3. As pointed out above, the location may vary substantially from this position, and the use of the wordapp oximatelyl is to be understood in that sense.

It is a familiar fact to those engaged in the that the tilting action described in connection against the lens is shaped by the same method as is employed in shaping pitch laps. I prefer to carry the melting of these chips just so far that the uppermost chips are not fully melted, so that, after the forming of the face of the lap, the surface of the cellulose acetate .is covered with cracks. I have also found that such laps may be grooved in much the same way as pitch laps are grooved. Such laps have a considerable amount of .cold flow which is characteristic of pitch, but this cold flow of the acetate lap may be increased by application to the surface of a small amount of swelling agent or plasticizer with some solvent action. 1

I have used the term "lower lap and upper lap to indicate respectively the lap which has rotary motion about its axis and the lap which is oscillated or moved conically about a flxedcenter. In the claims, the words lower and upper are to be construed in this sense and not necessarily as meaning that the one lap must be below the other.

The conical motion about the point P which the machine shown in Figure 6 provides can be looked upon'as a compounding of two simple oscillations in two planes at and with phases apart. For convenience, in the claims I shall use the word oscillation to mean either a s mple oscillation or any compounding of such oscillations so as to produce conical motions or any other type obtainable by such compounding I have described the general nature of this invention and have also described some particular embodiments of the invention in the form of pract cal machines for finishing of lens surfaces (by finishing is meant any of the operations: smooth grinding, fine grinding, polishing).

While specific embodiments of mach nes for carrying out my invention have been described, it is to be understood that variations in structural detail are contemplated within the scope of the claims. There is no intention of lim tation to the exact details shown and described;

Iclaim: v

1. A method of finishing opposite surfaces of a lens simultaneously and substantially to the same lens polishing industry that, during the polishing operation (with laps faced with pitch and with rouge mud as a medium), a considerable amount of suction and friction develops between the surface of the lens and the surface of the pitch lap.

When this suction becomes excessive. t is com-- mon practice to groove the surfaceof the pitch lap and the grooving is so made as to create larger pressures Where they are desired in the course of polishing. A feature in conventional lens polishing methods which has not apparently been hitherto recognized, however,: is the fact extent, comprising providin laps each having a finishing surface of the lens surface with which it is to engage, positioning said lens between said finishing surfacesso that its respective surfaces are in pressure engagement with the respective complementally-shaped finishing surfaces of said laps, and, while maintaining said pressure, rotating one of said finishing surfaces about a fixed axis, and simultaneously oscillating the other of said finishing surfaces about a pivot point determined approximately by Formula 3 of the specification whereby the relative motion between said finishing surfaces on said lens surfaceswill effect said finishing of both said lens surfaces.

2. A method of finishing opposite surfaces of shaped complemental to that of the specification whereby the relative motion between said finishing surfaces on said lens surfaces will eifect said finishing of both said lens surfaces.

3. A method of finishing opposite surfaces of a lens simultaneously and substantially to the same extent, comprising providing members having oppositely disposed finishing surfaces each-complemental to that of the lens surface with which it is to engage, positioning said lens between said finishing surfaces so that the respective lens surfaces are in pressure engagement with the respective complementally-shaped finishing surfaces, and while maintaining said pressure engagement, rotating one of said finishing surfaces about a fixed axis and simultaneously moving the other finishing surface so that an axis passing through the latter moves about a pivot point determined approximately by Formula 3 of the specification to describe a cone whose cone angle varies periodically whereby the relative motion between said finishing surfaces on said lens surfaces will effect said finishing of both said lens surfaces.

4. A method of finishing opposite surfaces of a lens having substantially different thickness through its center than at its periphery simultaneously and substantially to the same extent,

comprising providing members having oppositelydisposed that of the lens surface gage, positioning said lens between said-finishing surfaces so that the respective lens surfaces finishing surfaces each complemental to with which it is to enasrnsos and substantially to the same extent, the position of said lens between the surfaces of said lap being at all times uniquely determined by the coaction of thelens and said surfaces.

6. In apparatus for the finishing of oppositesurfaces of a lens simultaneously and substantially to the same extent, oppositely disposed laps having finishing surfaces between which the said lens is positioned, means for supporting one of said laps, means for adjusting the position of .said one of said laps with respect to the other of said laps, means for rotating said one of said laps about a central axis, universally pivoted means for supporting the other of said laps, means for moving said other of said laps to efiect motion thereof about a center provided by said universally pivoted means and determined approximately by Formula '3 0f the specification, whereby, when the said lens has its opposite surfaces engaged by said respective finishing surfaces, said rotation of the said first of said laps and the said motion of the other of said laps about its said determined center will cause said finishing surfaces to effect said finishing of said lens surfaces.- v

7. Apparatus for finishing the oppositely directed surfaces of a lens simultaneously'and substantially to the same extent comprising a lap having a finishing surface complemental in shape to that of one surface of said lens, means for rotating said lap about a fixed axis, means for adjusting said lap along said axis, a second lap having an oppositely directed finishing surface complemental in shape to the other surface of said lens, said finishing surfaces being adapted to receive between them the said lens, axially slidable means for carrying said second lap, universally pivoted means for supporting said axially slidable means, and means for imparting oscillatory rotary motion to said axially slidable means about I a center provided by said universally pivoted are in pressure engagement with the respective complementally-shaped finishing surfaces of said members, and, while maintaining said pressure engagement, rotating one of said finishing surfaces about a fixed axis, and simultaneously moving the other of said finishing surfaces along an orbital path that varies periodically in amplitude whereby the relative motion between said finishing surfaces on said lens surfaces will effect rotary and oscillating motion of the lens and said finishing of both said lens surfaces while the position of the lens between said finishing surfaces will at all times be uniquely determined by virtue of the kinematic reactions between coacting surfaces of the lens and the laps.

5. In apparatus of thecleZss described, a first lap having a surface whose shape is complemental to that desired on one face of a lens of relatively high curvature, a second lap having a surface complemental to that desired on the opposite face of said lens, means for rotating the first of means and determined approximately by Formula 3 of the specification, whereby said slide means and said second lap have compound conical motion imparted thereto whose cone angle about said determined center varies periodically.

8. Apparatus for finishing opposite surfaces of a lens simultaneously and to substantially the same extent comprising a lap having a finishing surface, means for rotating said lap about a fixed axis, a second lap having an oppositely directed finishing surface, said finishing surfaces bein adapted to receive between them the said lens,

axially slidable means for carrying said second lap, universally pivoted means for supporting said axially slidable means, means for imparting oscillatory rotary motion to said axially slidable means abouta center provided by said universally pivoted means,and determined approximately by Formula 3 of the specification, whereby said slide means and said second lap supported thereon have compound conical motion imparted thereto whose cone angle varies periodically about said detersaid laps about a central axis, means for imparting an oscillatory motion to the second of said laps about a center determined by the shape of the said faces ofsaid lens and approximately by Formula 3 of the specification, and means for pressing said surfaces against said faces of said lens to, finish said opposite faces simultaneously mined center.

9. Apparatus as per claim 5 in which a receptacle is provided in association with said laps adapted to contain finishing media, said receptacle being so positioned'that its contents are agitated by the movement of said laps and distributed directly to said lap surfaces.

10. Apparatus as per claim 5 in which means are provided for supplying finishing media to-said lap surfaces during finishing operations by said laps.

11. Apparatus for finishing the opposite surfaces of .a lens having substantially difl'erent thickness through its center than at its periphery simultaneously and substantially to the same extent, comprising a lap having a finishing surface, means for rotating said lap about a fixed axis, a second laphaving an oppositely directed finishing surface, said ,flnishing surfaces being adapted to receive the said lens between them, axially slidable means for carrying said second lap, pivoted means for supporting said axially slidable means, means for imparting rotary motion tosaid slidable said oceillatory member to said second gear.

12.111 apparatus for the finishing of opposite surfaces of a lens simultaneously and substantially to the same extent, a lower. lap and an upper lap having finishing surfaces between which the means and motion to the said second lap suping motion to said second lap comprising a stationary gear, a second gear movable around said stationary gear with planetary motion, a rotatable member carrying said second gear, means for ro-.

tating said rotatable member, an oscillatory member supported from said rotatable member, means specification.

said lens is positioned, means for supporting said lower lap and for adjusting itsposition relative to the upper lap, means for rotating said lower --lap about its axis, universally pivoted means for supporting the upper lap and means for movin it about the center provided by said universally pivoted means and determined approximately by Formula 3 of the specification, whereby when said lens has its opposite surfaces engaged by said respective finishin surfaces, the rotation of the lower lap and the motion of the upper lap about the said center will cause the finishing surfaces to effect the finishing of said lens surfaces.v

13. In a lens finishing machine, a pair of oppositely disposed laps having finishing surfaces,

complemental tothe lens surfaces to be finished, means for rotating one of said laps and means for oscillating the other or said laps about a point determined approximately by Formula 3 of the BENJAMIN Lmaowrrz. 

